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igor_vitrenko [27]
3 years ago
15

(X^4+5x^2-36)(2x^2+9x-5)=0 solve for the roots. Factor both quadratic equations

Mathematics
2 answers:
Novosadov [1.4K]3 years ago
8 0
Hello,

1)
X^4+5x²-36=0
Δ=5²+4*36=169=13²
x²=(-5-13)/2=-9 or x²=(-5+13)/2=4
x^4+5x²-36=(x²+9)(x²-4)=(x-2)(x+2)(x²+9)

2)
2x²+9x-5=0
Δ=9²+4*5*2=121=11²
x=(-9-11)/4=-5 or x=(-9+11)/4=1/2

2x²+9x-5=(x+5)(2x-1)

(x^4+5x^2-36)(2x^2+9x-5)=(x+5)(2x-1)(x+2)(x-2)(x²+9)

iren [92.7K]3 years ago
5 0
Using trial and error
x^4+5x^2-36 factors to (x-2)(x+2)(x^2+9)
2x^2+9x-5 factors to (x+5)(2x-1)
so

(x-2)(x+2)(x^2+9)(x+5)(2x-1)=0

set each to zero
x-2=0
x=2

x+2=0
x=-2

x^2+9=0
x^2=-9
x=3√-1
x=3i

x+5=0
x=-5

2x-1=0
2x=1
x=1/2=0.5



roots are
x=-5-2,0.5,2, and the imaginary root 3i
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Answer and Step-by-step explanation:

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Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

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Answer and explanation for each part of the question are as follow:

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Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

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b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

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P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

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P(X)=0.020  

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